Consistent Regularization of Induced Coulomb Stresses in Displaced Faults

This note provides unregularized and regularized closed-form analytical expressions for the depletion-induced or injection-induced pre-slip Coulomb stresses in two-dimensional displaced dip-slip faults. The regularization serves to remove logarithmic singularities and jump-discontinuities in the unregularized formulation. The expressions are identical to those in Appendices A and B of Jansen & Meulenbroek (2022): Netherlands Journal of Geosciences 101 e13, except for the correction of a small error in the regularized formulation. In numerical examples the difference of the correction is hardly noticeable, but it ensures that the corrected formulation is internally consistent in the sense that integrals of stresses and pressure along a fault are identical for the unregularized and regularized expressions.